Terahertz (THz) spectroscopic properties of two explosives and related compounds (ERCs), 2,4-Dinitrotoluene (DNT) and 2,6-DNT, and a non-ERC, para-Aminobenzoic acid (PABA) were studied using computational chemistry, focusing particularly at the region of 0 to 3 THz. Many ERCs have unique fingerprint absorption in the THz region, allowing their unambiguous identification. Density functional theory (DFT) was employed to study these low frequency THz peaks arising from intermolecular interactions. The theoretical approach taken in this thesis aims to acquire knowledge systematically through progressive inclusion of intermolecular interactions via the modeling of monomer, dimer and tetramer systems. All observed spectral peaks of the THz spectra of solid 2,4-DNT, 2,6-DNT and PABA are assigned, providing information on origins of the vibrational modes. Vibrational frequency analysis reveals that intermolecular vibrational modes and intermolecular vibrations coupled with intramolecular vibrational modes are responsible for the absorption peaks in the THz region. The assignment of observed vibrational frequencies in the THz region is heavily reliant on having a good knowledge of crystal structure and selecting a theoretical method that can aptly describe the intermolecular interactions present in the crystal structures.